Electronic Circular Dichroism of Transition Metal Complexes within TDDFT

1. Electronic Circular Dichroism of Transition Metal Complexes within TDDFT Jing Fan University of Calgary

2. Objectives • To understand, experimental CD spectra, quantum mechanical calculations of electronic structure and CD based on TDDFT • To elucidate the origin of CD in typical transition metal complexes, relationship between CD and molecular geometry • To evaluate the reliability and accuracy of TDDFT for transition metal compounds

3. Complexes Studied: Trigonal Dihedral: − -bonded complexes: [M(en)3]3+ (M = Co, Cr) (d-to-d, LMCT) − both - and π-bonded complexes: [M(L-L)3]n+ (M = Co, Cr; L =ox, acac, thiox, etc.) (d-to-d, LMCT, MLCT, LC) − complexes with conjugated ligands: [M(L-L)3]2+ ( M = Fe, Ru, Os; L = bpy, phen) (LC exciton CD ) Trigonal bipyramidal: − complexes with conjugated ligands [M(L)X]+ (M = Cu, Zn; L = MeTPA, MeBQPA, MeTQA; X = Cl-, NCS-) (LC exciton CD)

4. Computational Details ADF package • Basis sets (STO): • ligand atoms: frozen core triple- polarized “TZP” -C, N, O (1S); S (2p) • metal atoms: • -Co, Cr : TZP (2p); • -Fe, Ru, Os: TZ2P (2p, 3d, 4f) • Functionals: VWN (LDA) + BP86 (GGA) • Relativistic effect for Fe group metals (scalar ZORA) • Un-restricted calculations for Cr(III) • The “COnductor-like continuum Solvent MOdel” (COSMO) of solvation

5. -bonded Complexes : [Co(en)3]3+ and [Cr(en)3]3+ en: • Calculated E are systematically overestimated for the d-d region (by ~5,500 cm-1); underestimated for the LMCT region (by ~6,000 cm-1) d-d LMCT

6. Assignment of Transitions Lowest singlet excited states andtheir splitting in D3 symmetry Λ-[Co(en)3]3+ (2A2) (1E) (2E) (1A2) (3E)

7. Why Optically Active? 1A1g1T1g d-d transitions: magnetically allowed 1A1g1T1u LMCT transitions: electrically allowed Rotatory Strengths: electric transition dipole moment magnetic transition dipole moment

8. Metal d-orbitals: Origin of Optical Activity Symmetry Metal and Ligand Frontier Orbitals • Metal-ligand orbital interactions L-orbitals: 8 • Metal-ligand Orbital Interaction • Metal-ligand Orbital Interaction

9. Overlaps Expression , , , , s s s s s s = - + = + ˆ ˆ 1 e ( 3 / 2 ) 1 e ( 1 / 2 ) 2 e , 2 e ( 1 / 2 ) 1 e ( 3 / 2 ) 2 e Semi-quantitative Metal-ligand Orbital Overlaps In general Overlaps Case I Case II Case III Case I: Oh,  = 60 Case II: D3,  = −6.3 Case III: D3,  = +6.3 , 1.225 S 1.220 S 1.193 S -[Co(en)3]3+ , 0 -0.001 S 0.013 S 0 0.047 S 0.287 S , 0 0.096 S -0.102 S , 0 -0.021 S -0.160 S

10. MO diagram Energy (eV) MOs as linear combinations of symmetry ligand and metal d-orbitals Main components from DFT calculations bonding anti-bonding anti-bonding 10

11. positive negative s s ˆ 2 e ˆ 1 e y x • Prediction of the Sign of Rotatory Strengths Band 2: and in terms of one-electron excitations 4e(d) 5e(d)

12. Metal d-orbitals: Both - and π-bonded Complexes Metal and Ligand Frontier Orbitals L-orbitals: L-orbitals: 12 • Metal-ligand Orbital Interaction • Metal-ligand Orbital Interaction

13. overlap overlap* Symmetry Unique Metal-ligand Orbital Overlaps ,, . * Only p-orbitals on the N atoms are considered 13

14. Overlaps Overlaps Case I(Oh) Case I(Oh) Case II (D3) Case II (D3) -type -type 0.612 S 0.612 S 0.610 S 0.610 S 1.061 S 1.061 S 1.058 S 1.058 S 0 0 -0.034 S -0.034 S 0 0 -0.064 S -0.064 S 0 0 0.059 S 0.059 S -type -type 0 0 -0.138 S -0.138 S 0 0 0.110 S 0.110 S 1.632 S 1.632 S 1.590 S 1.590 S -0.816 S -0.816 S -0.892 S -0.892 S -2.002 S -2.002 S -1.976 S -1.976 S Case I: Oh Case II: D3

15. CD spectra - acac theor. expt. • d-to-d, LMCT as well as MLCT and LC, etc. • Global red-shift applied to the computed excitation energies: • Cr(III): –5.0  103 cm–1 • Co(III): –4.0  103 cm–1 15

16. - thiox

17. Early rule proposed for Λ-configuration: Azimuthal contraction ( < 0)  positive R(E) Polar compression (s/h > 1.22)  (E) < (A2) Relationship between CD of the d-d transitions and geometry in Λ-[M(L-L)3]n+ σ-bonded a Sign of rotatory strength of the E symmetry. b Azimuthal distortion; Δ = 0for ideal octahedrons. c Trigonal splitting of the T1g state. d Polar distortion; s/h = 1.22 for ideal octahedrons. 17

18. Rotatory strengths R ( ) and overlaps S(d2, ) ( ) against  (1E) (2E) R /10-40 cgs S / S S R(2E1) (1A2) R(1E1) / degree

19. Relationship between CD of the d-d transitions and geometry in Λ-[M(L-L)3]n+ a Sign of rotatory strength of the E symmetry. b Azimuthal distortion; Δ = 0for ideal octahedrons. c Trigonal splitting of the T1g state. d Polar distortion; s/h = 1.22 for ideal octahedrons. 19 19

20. Complexes with Conjugated Ligands (Trigonal Dihedral) Exciton CD (LC π-π* transitions) theor.  5 expt. E [Λ-Os(bpy)3]2+ M: Fe, Ru, Os N-N: bpy, phen For the Λ configuration: R(E) > 0, R(A2) < 0, υ(A2−E) > 0 A2

21. βπ Energy (eV) απ

22. (απ−>βπ) R(A2) < 0 and R(E) > 0 for 0 < < 90

23. Energy Splitting of CD Bands • d-to-d: trigonal splitting of dπ orbitals due to metal-ligand interactions • d-Lσ E polar compression (s/h > 1.22) (E) < (A2) [Co(en)3]3+ A2 E [Cr(en)3]3+ A2 • d-Lπ/σ E polar elongation (s/h < 1.22) (E) > (A2) Co(acac)3 and Cr(acac)3 A2

24. LC: trigonal splitting of dπ orbitals due to metal-ligand interactions and electron-electron repulsion energy involving different number of ligands

25. Determination of Absolute Configuration by CD • -bonded: d-to-d, LMCT ✔ • /-bonded: d-to-d (might be safe),CT (not safe) • /-bonded (conjugated ligands): LC excitonexcitations ✔ 25

26. Complexes with Tripodal Tetradentate Ligands (Trigonal bipyramidal) MeTPA MeBQPA MeTQA Cu Cu Cu